Actually I joined a company as a contractor as a software engineer consultant. They use clearcase.
I need to know what is the best way to be able to work with clearcase and understand it in few hours , one or two days to become comfortable with it. I don't have time to follow all the classical learning curve.
So if you can advice by giving:
- good book, reference, website, forum
- video presentation etc.

From a programmer's point of view what is the most important part that I should focus on when working with clearcase?

The developerWorks community does contain a forum, rss feeds and so on.
I don't think there is much one can miss regarding ClearCase there.

The most important parts are, of course, understanding the structure (this shouldn't be so hard to accomplish), and getting some acquaintance and routine with the core features, which are more or less standard in every ccm tool - and you mentioned them already in your post.

Don't waste too much time with the "mistakes to avoid" part. You will make mistakes, and you will learn the most by cleaning up afterwards.